NAG Library Function Document

nag_prob_normal_vector (g01sac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{ltail}$ – IntegerInput

On entry: the length of the array tail.

Constraint: $\mathbf{ltail}>0$.

2:    $\mathbf{tail}\left[\mathbf{ltail}\right]$ – const Nag_TailProbabilityInput

On entry: indicates which tail the returned probabilities should represent. Letting $Z$ denote a variate from a standard Normal distribution, and $z_i=\frac{x_i-{\mu }_i}{{\sigma }_i}$, then for $j=\left(\mathit{i}-1\right)\mathrm{ mod }\mathbf{ltail}$, for $\mathit{i}=1,2,\dots ,\max \left(\mathbf{lx},\mathbf{ltail},\mathbf{lxmu},\mathbf{lxstd}\right)$:

$\mathbf{tail}\left[j\right]=\mathrm{Nag\_LowerTail}$

The lower tail probability is returned, i.e., $p_i=P\left(Z\le z_i\right)$.

$\mathbf{tail}\left[j\right]=\mathrm{Nag\_UpperTail}$

The upper tail probability is returned, i.e., $p_i=P\left(Z\ge z_i\right)$.

$\mathbf{tail}\left[j\right]=\mathrm{Nag\_TwoTailConfid}$

The two tail (confidence interval) probability is returned, i.e., $p_i=P\left(Z\le \left|z_i\right|\right)-P\left(Z\le -\left|z_i\right|\right)$.

$\mathbf{tail}\left[j\right]=\mathrm{Nag\_TwoTailSignif}$

The two tail (significance level) probability is returned, i.e., $p_i=P\left(Z\ge \left|z_i\right|\right)+P\left(Z\le -\left|z_i\right|\right)$.

Constraint: $\mathbf{tail}\left[\mathit{j}-1\right]=\mathrm{Nag\_LowerTail}$, $\mathrm{Nag\_UpperTail}$, $\mathrm{Nag\_TwoTailConfid}$ or $\mathrm{Nag\_TwoTailSignif}$, for $\mathit{j}=1,2,\dots ,\mathbf{ltail}$.

3:    $\mathbf{lx}$ – IntegerInput

On entry: the length of the array x.

Constraint: $\mathbf{lx}>0$.

4:    $\mathbf{x}\left[\mathbf{lx}\right]$ – const doubleInput

On entry: $x_i$, the Normal variate values with $x_i=\mathbf{x}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lx}$.

5:    $\mathbf{lxmu}$ – IntegerInput

On entry: the length of the array xmu.

Constraint: $\mathbf{lxmu}>0$.

6:    $\mathbf{xmu}\left[\mathbf{lxmu}\right]$ – const doubleInput

On entry: ${\mu }_i$, the means with ${\mu }_i=\mathbf{xmu}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lxmu}$.

7:    $\mathbf{lxstd}$ – IntegerInput

On entry: the length of the array xstd.

Constraint: $\mathbf{lxstd}>0$.

8:    $\mathbf{xstd}\left[\mathbf{lxstd}\right]$ – const doubleInput

On entry: ${\sigma }_i$, the standard deviations with ${\sigma }_i=\mathbf{xstd}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lxstd}$.

Constraint: $\mathbf{xstd}\left[\mathit{j}-1\right]>0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{lxstd}$.

9:    $\mathbf{p}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, of the array p must be at least $\max \left(\mathbf{lx},\mathbf{ltail},\mathbf{lxmu},\mathbf{lxstd}\right)$.

On exit: $p_i$, the probabilities for the Normal distribution.

10:  $\mathbf{ivalid}\left[\mathit{dim}\right]$ – IntegerOutput

Note: the dimension, dim, of the array ivalid must be at least $\max \left(\mathbf{lx},\mathbf{ltail},\mathbf{lxmu},\mathbf{lxstd}\right)$.

On exit: $\mathbf{ivalid}\left[i-1\right]$ indicates any errors with the input arguments, with

$\mathbf{ivalid}\left[i-1\right]=0$

No error.

$\mathbf{ivalid}\left[i-1\right]=1$

On entry,

invalid value supplied in tail when calculating $p_i$.

$\mathbf{ivalid}\left[i-1\right]=2$

On entry,

${\sigma }_i\le 0.0$.

11:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_ARRAY_SIZE

On entry, $\mathbf{ltail}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ltail}>0$.

On entry, $\mathbf{lx}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lx}>0$.

On entry, $\mathbf{lxmu}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lxmu}>0$.

On entry, $\mathbf{lxstd}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lxstd}>0$.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NW_IVALID

On entry, at least one value of tail or xstd was invalid.
Check ivalid for more information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01sace.c)

10.2

Program Data

Program Data (g01sace.d)

10.3

Program Results

Program Results (g01sace.r)